On the transport capacity of the many-to-one dense wireless network

We consider dense wireless sensor networks deployed to observe arbitrary random fields. The requirement is to reconstruct an estimate of the random field at a certain collector node. This creates a many-to-one data gathering wireless channel. In this paper, we characterize the transport capacity of many-to-one dense wireless networks subject to a constraint on the total average power. In particular, we show that the transport capacity scales as ⊗(log(N)) when the number of sensors N grows to infinity and the total average power remains fixed. To prove the achievability of this result, we devise a simple constructive approach for realizing this capacity based on an antenna sharing idea. Interestingly, this constructive approach shows that one can achieve a transmission rate of the same order as the transport capacity with single user receivers. The transport capacity result is independent of where the traffic is generated in the network. Moreover, we show that the same scaling law holds even if every node has a constant non-vanishing average power. As argued in the sequel, our results may have some important implications on the design of dense sensor networks.